A self-consistent, two-dimensional model of subsonic, plasma sheet convection is presented. Specifically, time sequences of static equilibrium solutions for the two-dimensional magnetospheric magnetic field are constructed consistent with adiabatic convection. This model self-consistently includes a dipole field and a reasonable accounting for the effects of inner magnetospheric shielding. Starting from a relaxed magnetospheric equilibrium, the earthward convection of plasma sheet flux tubes results in the stretching of inner plasma sheet field lines, the development of a local minimum in the equatorial magnetic field Be in the near-Earth plasma sheet, and an increasing lobe magnetic field. This evolution in time occurs generally, independent of the specific magnetopause or far-tail boundary conditions, provided the plasma sheet is not at marginal interchange stability. This behavior results solely from the convection of flux tubes of increasing entropy into the near-Earth plasma sheet. We discuss these results in the general context of earthward convection in Earth's plasma sheet and in the specific context of magnetospheric substorms. ¿ American Geophysical Union 1992